Police holding three men on suspicion of kidnap and rape of a toddler believe there were attempts to entice other children into a car on the same day.
The men are being held in Cardiff after the girl was abducted from her home in the Rumney area of the city on Monday.
Police said two men in a dark Ford Escort may have been in nearby Llanrumney between 0500 and 2300 GMT.
Detectives have appealed for anyone who saw the car or anyone who was invited to get inside it, to contact them.
South Wales Police Detective Superintendent Paul Kemp, who is leading the investigation, said: "We have reason to believe that the two men in question may have attempted to entice young girls into their car at some stage during Monday, 2 January.
Police chiefs want to speak to anyone who saw the Ford Escort
"I am appealing to anyone who had any contact with these men to speak to us at the incident room. They may have information that is vital to the investigation."
One girl, older than the three-year-old, has told police that she was approached by two men in a car as she walked along a road in Rumney with friends.
Some time after police say the three-year-old girl was raped after being taken - not lured or coaxed - from inside her home sometime between 1900 and 2300 GMT on Monday.
It was the start of an 80-mile road trip in which she was driven along the M4, out of Wales, and then along the motorway to Swindon.
In the early hours of Tuesday morning - after two men aged 34 and 47 had been arrested in south Wales - an alert was put out for a car which was spotted going through a red traffic light in Wiltshire.
It was pursued and crashed on the A4 between Hungerford and Marlborough.
The 26-year-old driver was arrested and the three-year-old was airlifted to hospital. Police said she was not badly hurt in the collision but had sustained other significant injuries.
House-to-house inquiries are ongoing in Rumney
The child has since been released from hospital and is with her mother but has refused to return to her home.
Detectives have been given more time to question the three men and a forensic examination is continuing at a property in Newport.
Gwent Probation Service confirmed that the property was used to house newly-released prisoners.
And Northumbria Police investigating the abduction of a six-year-old girl in Tyneside, confirmed they are liaising with detectives in south Wales.
For over a week they have been trying to trace a man who snatched the girl from the bath and left her screaming and naked in an alley. She had been sexually assaulted.
Speaking to BBC Wales on Thursday, a member of three-year-old's family said she is "okay under the circumstances" and did not really understand what had happened.
The relative added that the child was "very quiet and hasn't said very much at all".
Officers are continuing house-to-house inquiries in Rumney and said they were pursuing "a number of lines of inquiry".
Deputy divisional commander for Cardiff superintendent Josh Jones, said he recognised the concern among residents of Rumney.
However, he added: "I must emphasise that we have recovered a car and we have three people in custody in respect of the kidnap and rape investigation - we are not currently looking for anyone else in relation to this matter.
"Incidents like this are extremely rare and we will continue to provide a highly visible police presence in the area."
Anyone with information is urged to contact the incident room on 02920 222111 or Crimestoppers anonymously on 0800 555111.